G. A. Mikhailov, A. S. Korda, S. V. Rogazinskii, “Comparative analysis of various numerically statistical projection algorithms for the solving the transfer theory problems”, Dokl. RAN. Math. Inf. Proc. Upr., 2022, Volume 502,Pages <nobr>42

MATHEMATICS

Comparative analysis of various numerically statistical projection algorithms for the solving the transfer theory problems

G. A. Mikhailov^ab, A. S. Korda^a, S. V. Rogazinskii^ab

^a Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: A comparative analysis of various variants of the Monte Carlo projective algorithm for estimating the particles flow through a layer of medium with scattering of the Henyey–Greenstein type is carried out. The possibility of minimizing the mean-square error by equalizing the corresponding stochastic and deterministic terms is investigated.

Keywords: Monte Carlo method, projection estimator, mean-square error, collision estimator, direct simulation, Laguerre polynomials, Henyey–Greenstein indicatrix.

UDC: 519.642

Received: 29.10.2021
Revised: 29.10.2021
Accepted: 20.12.2021

DOI: 10.31857/S2686954322010106